Permutation and Combination

(6) How many different three-digit numbers can be formed using the digits 1, 2, 3, and 4 without repetition?

• (a) 12
• (b) 24
• (c) 36
• (d) 48

Answer

Correct Answer: (b) 24
The number of different three-digit numbers that can be formed using the digits 1, 2, 3, and 4 without repetition is ^{4}P_{3} = \frac{4!}{(4-3)!} = 24 .

(7) How many ways can you arrange the letters of the word “COMBINE”?

• (a) 720
• (b) 2520
• (c) 10080
• (d) 5040

Answer

Correct Answer: (c) 10080
The number of ways to arrange the letters of the word “COMBINE” is ^{7}P_{7} = 7! = 10080 .

(8) In how many ways can you select 2 red balls and 3 green balls from a bag containing 5 red balls and 4 green balls?

• (a) 30
• (b) 60
• (c) 45
• (d) 15

Answer

Correct Answer: (b) 60
The number of ways to select 2 red balls and 3 green balls from a bag containing 5 red balls and 4 green balls is ^{5}C_{2} \times ^{4}C_{3} = \frac{5!}{2!(5-2)!} \times \frac{4!}{3!(4-3)!} = 60 .

(9) How many 3-letter words can be formed from the word “MATH” if repetition of letters is not allowed?

• (a) 24
• (b) 36
• (c) 12
• (d) 18

Answer

Correct Answer: (d) 18
The number of 3-letter words that can be formed from the word “MATH” without repetition is ^{4}P_{3} = \frac{4!}{(4-3)!} = 18 .

(10) In how many ways can you choose 4 items from a set of 8 different items, where the order of selection does not matter?

• (a) 70
• (b) 56
• (c) 28
• (d) 84

Answer

Correct Answer: (a) 70
The number of ways to choose 4 items from a set of 8 different items without considering the order of selection is given by ^{8}C_{4} = \frac{8!}{4!(8-4)!} = 70 .